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Ideas of Stephen Read, by Text
[British, fl. 2001, Professor at St Andrew's University.]
1994
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Formal and Material Consequence
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'Logic'
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p.245
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14187
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If logic is topic-neutral that means it delves into all subjects, rather than having a pure subject matter
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'Logic'
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p.245
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14188
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Not all arguments are valid because of form; validity is just true premises and false conclusion being impossible
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'Reduct'
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p.240
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14182
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If the logic of 'taller of' rests just on meaning, then logic may be the study of merely formal consequence
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'Repres'
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p.243
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14184
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In modus ponens the 'if-then' premise contributes nothing if the conclusion follows anyway
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'Repres'
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p.244
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14186
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Logical connectives contain no information, but just record combination relations between facts
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'Repres'
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p.244
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14185
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Conditionals are just a shorthand for some proof, leaving out the details
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'Suppress'
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p.242
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14183
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Maybe arguments are only valid when suppressed premises are all stated - but why?
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1995
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Thinking About Logic
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Ch.1
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p.9
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10966
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A proposition objectifies what a sentence says, as indicative, with secure references
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Ch.2
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p.35
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10970
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A theory of logical consequence is a conceptual analysis, and a set of validity techniques
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Ch.2
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p.39
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10971
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A logical truth is the conclusion of a valid inference with no premisses
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Ch.2
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p.41
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10972
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The non-emptiness of the domain is characteristic of classical logic
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Ch.2
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p.43
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10973
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A theory is logically closed, which means infinite premisses
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Ch.2
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p.43
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10974
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Compactness is when any consequence of infinite propositions is the consequence of a finite subset
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Ch.2
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p.43
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10975
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Compactness does not deny that an inference can have infinitely many premisses
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Ch.2
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p.44
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10977
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Compactness blocks the proof of 'for every n, A(n)' (as the proof would be infinite)
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Ch.2
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p.44
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10976
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Compactness makes consequence manageable, but restricts expressive power
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Ch.2
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p.47
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10979
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Although second-order arithmetic is incomplete, it can fully model normal arithmetic
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Ch.2
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p.47
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10978
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In second-order logic the higher-order variables range over all the properties of the objects
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Ch.2
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p.49
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10980
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Second-order arithmetic covers all properties, ensuring categoricity
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Ch.2
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p.51
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10982
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How can modal Platonists know the truth of a modal proposition?
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Ch.2
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p.51
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10981
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A possible world is a determination of the truth-values of all propositions of a domain
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Ch.2
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p.52
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10983
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Knowledge of possible worlds is not causal, but is an ontology entailed by semantics
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Ch.2
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p.53
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10984
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Logical consequence isn't just a matter of form; it depends on connections like round-square
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Ch.2
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p.54
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10985
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We should exclude second-order logic, precisely because it captures arithmetic
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Ch.2
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p.54
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10986
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Not all validity is captured in first-order logic
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Ch.2
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p.59
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10987
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Three traditional names of rules are 'Simplification', 'Addition' and 'Disjunctive Syllogism'
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Ch.2
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p.62
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10988
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Any first-order theory of sets is inadequate
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Ch.3
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p.66
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10989
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The standard view of conditionals is that they are truth-functional
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Ch.3
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p.72
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10992
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The point of conditionals is to show that one will accept modus ponens
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Ch.4
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p.101
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10995
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A haecceity is a set of individual properties, essential to each thing
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Ch.4
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p.106
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10997
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Von Neumann numbers are helpful, but don't correctly describe numbers
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Ch.4
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p.106
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10996
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Actualism is reductionist (to parts of actuality), or moderate realist (accepting real abstractions)
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Ch.4
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p.107
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10998
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The mind abstracts ways things might be, which are nonetheless real
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Ch.4
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p.117
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11000
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If worlds are concrete, objects can't be present in more than one, and can only have counterparts
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Ch.4
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p.118
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11001
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Equating necessity with truth in every possible world is the S5 conception of necessity
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Ch.4
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p.118
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11004
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Necessity is provability in S4, and true in all worlds in S5
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Ch.5
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p.123
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11005
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Negative existentials with compositionality make the whole sentence meaningless
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Ch.5
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p.125
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11007
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Quantifiers are second-order predicates
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Ch.5
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p.133
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11011
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Same say there are positive, negative and neuter free logics
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Ch.5
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p.140
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11012
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A 'supervaluation' gives a proposition consistent truth-value for classical assignments
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Ch.5
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p.142
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11013
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Identities and the Indiscernibility of Identicals don't work with supervaluations
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Ch.6
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p.154
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11014
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Self-reference paradoxes seem to arise only when falsity is involved
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Ch.7
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p.178
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11016
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Would a language without vagueness be usable at all?
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Ch.7
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p.184
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11017
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Some people even claim that conditionals do not express propositions
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Ch.7
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p.189
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11018
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There are fuzzy predicates (and sets), and fuzzy quantifiers and modifiers
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Ch.7
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p.200
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11019
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Supervaluations say there is a cut-off somewhere, but at no particular place
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Ch.8
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p.214
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11020
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Realisms like the full Comprehension Principle, that all good concepts determine sets
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Ch.8
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p.236
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11025
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Infinite cuts and successors seems to suggest an actual infinity there waiting for us
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Ch.9
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p.229
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11024
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Semantics must precede proof in higher-order logics, since they are incomplete
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